Linear Operators, Part 2 |
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Page 2022
... measurable function defined on the spec- trum σ ( A ̧ ) = σ ( Â ) . We simply define the p xp matrix ƒ ( Â ) ( s ) whose elements are measurable functions on RN by the equation ƒ ( Â ) ( s ) f ( Â ( s ) ) . ( If the roots of the minimal ...
... measurable function defined on the spec- trum σ ( A ̧ ) = σ ( Â ) . We simply define the p xp matrix ƒ ( Â ) ( s ) whose elements are measurable functions on RN by the equation ƒ ( Â ) ( s ) f ( Â ( s ) ) . ( If the roots of the minimal ...
Page 2193
... functions on the space of maximal ideals in A , and if E is the resolution of the identity for T , B is also equivalent to the algebra of all E - essentially bounded Borel measurable functions on the spectrum of T. This latter ...
... functions on the space of maximal ideals in A , and if E is the resolution of the identity for T , B is also equivalent to the algebra of all E - essentially bounded Borel measurable functions on the spectrum of T. This latter ...
Page 2410
... measurable function defined in D x D , with values in the space B ( X ) of ... functions defined in D and satisfying ( 33 ) . Let 1 / pl / p'1 . Let e1 ... functions f such that f ( z ) = X ; for all zee ,, 1 ≤ j < ∞ . Let T be the ...
... measurable function defined in D x D , with values in the space B ( X ) of ... functions defined in D and satisfying ( 33 ) . Let 1 / pl / p'1 . Let e1 ... functions f such that f ( z ) = X ; for all zee ,, 1 ≤ j < ∞ . Let T be the ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero